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Locally Finite Root Systems
 
Ottmar Loos University of Innsbruck, Innsbruck, Austria
Erhard Neher University of Ottawa, Ottawa, ON, Canada
Front Cover for Locally Finite Root Systems
Available Formats:
Electronic ISBN: 978-1-4704-0412-3
Product Code: MEMO/171/811.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
Front Cover for Locally Finite Root Systems
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  • Front Cover for Locally Finite Root Systems
  • Back Cover for Locally Finite Root Systems
Locally Finite Root Systems
Ottmar Loos University of Innsbruck, Innsbruck, Austria
Erhard Neher University of Ottawa, Ottawa, ON, Canada
Available Formats:
Electronic ISBN:  978-1-4704-0412-3
Product Code:  MEMO/171/811.E
List Price: $60.00
MAA Member Price: $54.00
AMS Member Price: $36.00
  • Book Details
     
     
    Memoirs of the American Mathematical Society
    Volume: 1712004; 214 pp
    MSC: Primary 17; 20;

    We develop the basic theory of root systems \(R\) in a real vector space \(X\) which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: The intersection of \(R\) with every finite-dimensional subspace of \(X\) is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

    Readership

    Graduate students and research mathematicians interested in infinite-dimensional Lie theory.

  • Table of Contents
     
     
    • Chapters
    • Introduction
    • 1. The category of sets in vector spaces
    • 2. Finiteness conditions and bases
    • 3. Locally finite root systems
    • 4. Invariant inner products and the coroot system
    • 5. Weyl groups
    • 6. Integral bases, root bases and Dynkin diagrams
    • 7. Weights and coweights
    • 8. Classification
    • 9. More on Weyl groups and automorphism groups
    • 10. Parabolic subsets and positive systems for symmetric sets in vector spaces
    • 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group
    • 12. Closed and full subsystems of finite and infinite classical root systems
    • 13. Parabolic subsets of root systems: classification
    • 14. Positive systems in root systems
    • 15. Positive linear forms and facets
    • 16. Dominant and fundamental weights
    • 17. Gradings of root systems
    • 18. Elementary relations and graphs in 3-graded root systems
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Volume: 1712004; 214 pp
MSC: Primary 17; 20;

We develop the basic theory of root systems \(R\) in a real vector space \(X\) which are defined in analogy to the usual finite root systems, except that finiteness is replaced by local finiteness: The intersection of \(R\) with every finite-dimensional subspace of \(X\) is finite. The main topics are Weyl groups, parabolic subsets and positive systems, weights, and gradings.

Readership

Graduate students and research mathematicians interested in infinite-dimensional Lie theory.

  • Chapters
  • Introduction
  • 1. The category of sets in vector spaces
  • 2. Finiteness conditions and bases
  • 3. Locally finite root systems
  • 4. Invariant inner products and the coroot system
  • 5. Weyl groups
  • 6. Integral bases, root bases and Dynkin diagrams
  • 7. Weights and coweights
  • 8. Classification
  • 9. More on Weyl groups and automorphism groups
  • 10. Parabolic subsets and positive systems for symmetric sets in vector spaces
  • 11. Parabolic subsets of root systems and presentations of the root lattice and the Weyl group
  • 12. Closed and full subsystems of finite and infinite classical root systems
  • 13. Parabolic subsets of root systems: classification
  • 14. Positive systems in root systems
  • 15. Positive linear forms and facets
  • 16. Dominant and fundamental weights
  • 17. Gradings of root systems
  • 18. Elementary relations and graphs in 3-graded root systems
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